Preheat the oven to 350 degrees F. Grease several baking sheets or coat with nonstick spray.

In a medium bowl, thoroughly stir together the flour, baking soda, and salt; set aside. In a large bowl, with an electric mixer on medium speed, beat together the butter, sugar, and brown sugar until very well blended, about 2 minutes. Add the egg and vanilla and beat until evenly incorporated. Beat in the banana, then the flour mixture, until evenly incorporated. Stir in the oats and chocolate morsets until evenly incorporated.

Using an ice cream scoop or spoons, drop the dough onto the baking sheets in scant golf-ball-sized mounds, spacing about 2-1/2 inches apart.

Bake the cookies, one sheet at a time, in the upper third of the oven for 10 to 14 minutes, or until lightly tinged with brown all over and almost firm when pressed in the centers. Reverse the sheet from front to back halfway through baking to ensure even browning. Transfer the sheet to a wire rack and let stand until the cookies firm up slightly, 2 to 3 minutes. Using a spatula, transfer the cookies to wire racks. Let stand until completely cooled.

These cookies are best when fresh but may be stored in an airtight container for up to 4 days or frozen for up to 1 month.

Tip
For the best flavor and texture, be sure to use an extremely ripe banana. One that is too soft and brown to eat fresh is ideal for this recipe.